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184                    ON THE COLOURS OF THICK PLATES.
SECTION IV.
Straight bands formed by a plane mirror at a considerable angle of incidence, and vieived by the eye, either directly, or through i                          a telescope.
'                             23.    As the angle of incidence increases the bands become
finer and finer, and after they have become too fine to be distinguished by the naked eye they may still be seen through a telescope, provided the source of light be sufficiently small. When the source of light was the image of the sun in a lens of short focus, I saw traces of the bands when the angle of incidence was about 24 50', but they were not at all well formed beyond an angle of about 10 40', after which they began to bo confounded with rays which shot in all directions from the image of the luminous point. With a mirror made of thinner glass they would probably have been visible at a still larger angle of incidence. The theory of Section II. sufficiently explains their origin and general character; but inasmuch as the obliquity was supposed small in investigating the formula of that section, it may be desirable to obtain an expression for their breadth, in which no approximation shall be *'                             made depending on the smallness of the obliquity, in order to
| j                            meet the case of any future measures which may be taken at a
large angle of incidence.
24. The notation being the same as in Art. 10, we have merely to employ the equations (17) and (18), without making any approximation depending on the smallness of <p and <'. The thickness t may still be supposed small compared with c and h. Neglecting t for a first approximation, and then substituting in the small terms the values of tan $' and sec <' got from the first approximation, we find
2*
.
8   T" C
Interchanging c and h, s and u, and subtracting, we get finally